On Using The Bmcsl Equation Of State To Renormalize The Onsager Theory Approach To Modeling Hard Prolate Spheroidal Liquid Crystal Mixtures

Modifications to the traditional Onsager theory for modeling isotropic-nematic phase transitions in hard prolate spheroidal systems are presented. Pure component systems are used to identify the need to update the Lee-Parsons resummation term. The Lee-Parsons resummation term uses the Carnahan-Starling equation of state to approximate higher-order virial coefficients beyond the second virial coefficient employed in Onsager's original theoretical approach. As more exact ways of calculating the excluded volume of two hard prolate spheroids of a given orientation are used, the division of the excluded volume by eight, which is an empirical correction used in the original Lee-Parsons resummation term, must be replaced by six to yield a better match between the theoretical and simulation results. These modifications are also extended to binary mixtures of hard prolate spheroids using the Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) equation of state.